Lift Equation
As you might expect there is a mathematical relationship between several factors that determine the ability of a wing to produce lift. These factors are coefficient of lift (Cl), velocity, air density and wing surface and can be expressed in the formula below (formula 1).

  • Cl - Coefficient of Lift
  • rho - Air density
  • V - Velocity
  • S - Wing surface area
Formula 1 - Lift equation  

By looking at the formula above it is obvious that for lift to increase one or more factors on the right side of the equal sign must increase. In the formula above ½ rho times the velocity squared basically stands for dynamic pressure. From here it is easy to understand that lift is proportional to the square of the velocity so doubling your airspeed will result in quadrupling the amount of lift, if everything else stays the same. Likewise, if all other factors remain the same while the coefficient of lift increases, lift will also increase. The coefficient of lift goes up as the angle of attack increases. Air density simply cannot be controlled but is of main concern as lift is diminished by reductions in air density, for example, when your climbing to higher altitudes or planning for take-off on a hot day. Air density is affected by temperature, altitude, humidity and barometric pressure. Wing surface area is fixed in clean configuration and is mostly variable by extending wing flaps and/or slats, i.e. larger wings generate more lift.

The equation described above can be used in another way by keeping the lift value at the same value and observe how the factors on the other side of the equation change and affect each other. On long-range flights, the weight of the airplane changes dramatically as a great amount of fuel is burned. This means that the amount of lift necessary to support its weight decreases as the flight progresses. In order to generate the right amount of lift that will keep the airplane flying straight and level the equation shows that the coefficient of lift, or angle of attack, must decrease. Likewise, if you increase the angle of attack you are able to fly the aircraft at a lower velocity thus making it possible to stay at the same altitude. Overall, we can say that the amount of lift depends on the interaction between angle of attack and true airspeed. Similarly, as we've discussed before, if density decreases as the aircraft gains height or temperature is high, the aircraft should be flown either with a higher angle of attack or higher true airspeed in order to generate the same amount of lift.

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